Based on the variable separation method, the Kadomtsev-Petviashvili equation is transformed into a system of equations, in which one is a fractional ordinary differential equation with respect to time variable $t$, and the other is an integer order variable coefficients partial differential equation with respect to spatial variables $x,y$. Assuming that the coefficients of the obtained partial differential equation satisfy certain conditions, the equation is further reduced. The extended homogeneous balance method is used to find the exact solutions of the reduced equation. According to the solutions of some special fractional ordinary differential equations, we obtain some hyperbolic function solutions of time-fractional Kadomtsev-Petviashvili equation with variable coefficients.